There is much to admire in Sheryl Sandberg's book, Lean In: Women, Work, and the Will to Lead. It is full of funny stories about her brilliant career and helpful advice for workplace success. As former chief of staff at the U.S. Treasury Department and vice-president of Google, and now COO of Facebook, the 43-year-old billionaire and mother of two has a lot of worldly wisdom to share. She is right that many women sell themselves short and pull back too early from their careers. Sandberg urges them to man up.

But this otherwise likeable and inspirational self-help book has a serious flaw: It is mired in 1970s-style feminism. Nation magazine columnist Katha Pollitt compares Sandberg to "someone who's just taken Women's Studies 101 and wants to share it with her friends." What Pollitt intends as a compliment goes to the heart of what is wrong with Lean In.

Sandberg envisions a time where gender roles all but disappear. "A truly equal world would be one where women ran half our countries and companies and men ran half our homes." She blames society for tricking little girls into liking princesses and little boys into preferring superheroes. "The gender stereotypes introduced in childhood are reinforced throughout our lives and become self-fulfilling prophesies."

Sandberg excels at the forward edge of economics and technology, but her sociology leans back to the Age of Aquarius. She praises to the skies Marlo Thomas's 1972 unisex album "Free to Be You and Me." She wants to bring back consciousness-raising groups, calling them "Lean in Circles." Women are advised to meet together and carry out "Listen, ask, and share" exercises. Sandberg's "Lean In" website provides "exploration kits" for these séances. One instructs group members to go round the room and finish sentences like "What I am most looking forward to in the month ahead..." and "Today I am feeling..." Is this how Mark Zuckerberg got to the top?

Sandberg's goal is to liberate her fellow Americans from the stereotypes of gender. But is that truly liberating? In a 2008 study in the Journal of Personality and Social Psychology, a group of international researchers compared data on gender and personality across 55 nations. Throughout the world, women tend to be more nurturing, risk averse and emotionally expressive, while men are usually more competitive, risk taking, and emotionally flat. But the most fascinating finding is this: Personality differences between men and women are the largest and most robust in the more prosperous, egalitarian, and educated societies. According to the authors, "Higher levels of human development—including long and healthy life, equal access to knowledge and education, and economic wealth—were the main nation-level predictors of sex difference variation across cultures." New York Times science columnist John Tierney summarized the study this way: "It looks as if personality differences between men and women are smaller in traditional cultures like India's or Zimbabwe's than in the Netherlands or the United States. A husband and a stay-at-home wife in a patriarchal Botswanan clan seem to be more alike than a working couple in Denmark or France."

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Why should that be? The authors of the study hypothesize that prosperity and equality bring greater opportunities for self-actualization. Wealth, freedom, and education empower men and women to be who they are. It is conspicuously the case that gay liberation is a feature of advanced, prosperous societies: but such societies also afford heterosexuals more opportunities to embrace their gender identities. This cross-cultural research is far from conclusive, but it is intriguing and has great explanatory power. Just think: What if gender difference turns out to be a phenomenon not of oppression, but rather of social well-being?

Consider, in this regard, the gender disparities in engineering. An article on the Wharton School website laments the paucity of women engineers and holds up China and Russia as superior examples of equity. According to the post, "In China, 40 percent of engineers are women, and in the former USSR, women accounted for 58 percent of the engineering workforce." The author blames workplace biases and stereotypes for the fact that women in the United States earn only 20 percent of the doctoral degrees in engineering. But perhaps American women earn fewer degrees in engineering because they don't have to. They have more opportunities to pursue careers that really interest them. American women may be behind men in engineering, but they now earn a majority of all Ph.Ds and outnumber men in humanities, biology, social sciences, and health sciences. Despite 40 years of consciousness-raising and gender-neutral pronouns, most men and women still gravitate to different fields and organize their lives in different ways. Women in countries like Sweden, Norway and Iceland enjoy elaborate supportive legislation, yet their vocational preferences and family priorities are similar to those of American women.

In a 2013 national poll on modern parenthood, the Pew Research Center asked mothers and fathers to identify their "ideal" working arrangement. Fifty percent of mothers said they would prefer to work part-time and 11 percent said they would prefer not to work at all. Fathers answered differently: 75 percent preferred full-time work. And the higher the socio-economic status of women, the more likely they were to reject full-time employment. Among women with annual family incomes of $50,000 or higher, only 25 percent identified full-time work as their ideal. Sandberg regards such attitudes as evidence of women's fear of success, double standards, gender bias, sexual harassment, and glass ceilings. But what if they are the triumph of prosperity and opportunity?

Sandberg seems to believe that the choices of contemporary American women are not truly free. Women who opt out or "lean back" (that is, towards home) are victims of sexism and social conditioning. "True equality will be achieved only when we all fight the stereotypes that hold us back." But aren't American women as self-determining as any in the history of humanity? In place of bland assertion, Sandberg needs to explain why the life choices of educated, intelligent women in liberal, opportunity-rich societies are unfree. And she needs to explain why the choices she promotes will make women happier and more fulfilled.

An up-to-date manifesto on women and work should steer clear of encounter groups and boys-must-play-with dolls rhetoric. It should make room for human reality: that in the pursuit of happiness, men and women often take different paths. Gender differences can sometimes be symptoms of oppression and subordination. But in a modern society they can also be the felicitous consequences of liberated choice—of the "free to be you and me" that women have been working towards for generations.